Advertisements
Advertisements
प्रश्न
State whether the following statement is True or False:
The equation of tangent to the curve y = 4xex at `(-1, (- 4)/"e")` is ye + 4 = 0
पर्याय
True
False
Advertisements
उत्तर
True.
Explanation:
y = 4x ex
∴ `"dy"/"dx" = 4"e"^"x" + 4"xe"^"x"`
Slope of the tangent at `(-1, (- 4)/"e")` is
`("dy"/"dx")_((-1, (- 4)/"e")` `= 4"e"^-1 + 4(-1)"e"^-1`
`= 4/"e" - 4/"e" = 0`
∴ Equation of the tangent at `(-1, (- 4)/"e")` is `("y" + 4/"e")` = 0(x + 1)
∴ ye + 4 = 0
APPEARS IN
संबंधित प्रश्न
Find the derivative of the following function from first principle.
(x – 1) (x – 2)
Find the derivative of the following function from first principle.
`1/x^2`
Find the equation of tangent and normal to the curve at the given points on it.
y = 3x2 - x + 1 at (1, 3)
Find the equation of tangent and normal to the curve at the given points on it.
2x2 + 3y2 = 5 at (1, 1)
Find the equations of tangent and normal to the curve y = x2 + 5 where the tangent is parallel to the line 4x − y + 1 = 0.
Find the equations of tangent and normal to the curve y = 3x2 - 3x - 5 where the tangent is parallel to the line 3x − y + 1 = 0.
Choose the correct alternative.
If 0 < η < 1, then demand is
Fill in the blank:
If f(x) = x - 3x2 + 3x - 100, x ∈ R then f''(x) is ______
State whether the following statement is True or False:
x + 10y + 21 = 0 is the equation of normal to the curve y = 3x2 + 4x - 5 at (1, 2).
Find the equation of tangent and normal to the following curve.
xy = c2 at `("ct", "c"/"t")` where t is parameter.
Find the equation of tangent and normal to the following curve.
y = x2 + 4x at the point whose ordinate is -3.
Find the equation of tangent and normal to the following curve.
x = `1/"t", "y" = "t" - 1/"t"`, at t = 2
Find the equation of tangent and normal to the following curve.
y = x3 - x2 - 1 at the point whose abscissa is -2.
The slope of the tangent to the curve y = x3 – x2 – 1 at the point whose abscissa is – 2, is ______.
Choose the correct alternative:
Slope of the normal to the curve 2x2 + 3y2 = 5 at the point (1, 1) on it is
The slope of the tangent to the curve x = `1/"t"`, y = `"t" - 1/"t"`, at t = 2 is ______
Find the equation of tangent to the curve x2 + y2 = 5, where the tangent is parallel to the line 2x – y + 1 = 0
Find the equation of tangent to the curve y = x2 + 4x at the point whose ordinate is – 3
Find the equation of tangent and normal to the curve y = x2 + 5 where the tangent is parallel to the line 4x – y + 1 = 0.
